Technology and Mathematics :an Introduction(MUST read)

Now why this technology blog when I already have one[here]? Well, to begin with technology is an interest of mine which deserves a category of its own. Hence, this blog. Now why only this technology blog? Well, first of all this blog will not be talking about gadgets , or how to fine tune and speed up your computer[or may be when I have nothing else to write about!] or other such tid-bits; it will talk about two guiding phenomena of technology.

(1) Underlying philosophy in technological advancement.

(2) The backbone of technology-mathematics.

To make matters less ambiguous let me state that when I refer to technology I usually talk about the net and IT revolution. So technology would mainly mean this, until otherwise stated specifically.

Also when I use the term mathematics I mean higher mathematics, and not in the general sense like – hey count nicely, do your maths.

As the complexity of cutting edge technology grows, it will be more and more dependent on mathematics. For many it would seem that this is the era of technology- well it is not. The era of technology is yet to come. Let me give you an analogy to illustrate my point. At the time of Aristotle and Archimedes[of the Eureka fame!] the era of Physics had begun, but it had not reached its mathematical finesse yet. There was a lot of accosting and dating which went between mathematics and physics, but the marriage of physics and mathematics took place with Newton acting as the head priest. And with the culmination of strong bond between mathematics and physics put forward by Einstein. You can call it an age of Physics if you want, but certainly not of technology. Technology is still in its ‘tinkering’ stage with now and then dates with mathematics. There have been many who have used the underlying power of mathematics to change the face of technology. To give you an example I choose the most popular technology[if not the best example to show the relation between mathematics and technology]—Google. It extensively used mathematics to harness the power of net in its new search engine- google.com. For further reading you can have a look at the paper written by Larry Page and Sergey Brin- co founders of Google-here.

Let me finish this introduction by paying tribute to the beauty of mathematics by the proof of infinitude of primes by Euclid.

 

Theorem:

 

There are infinitely many primes.

 

Proof:

Suppose that p1=2 < p2 = 3 < … < pr are all of the primes. Let P = p1p2pr+1 and let p be a prime dividing P; then p can not be any of p1, p2, …, pr, otherwise p would divide the difference Pp1p2pr=1, which is impossible. Hence either P itself is a prime number or any prime other than p1, p2,…, pr .Now if P is a prime then we get a contradiction as we assumed that pr is the largest prime. If there is any other prime number which divides P,say Q, then Q is other than p1, p2,… pr and hence greater than pr, because all the primes less then pr[namely p1, p1,… pr-1] are already excluded. Hence Q is a prime greater than p1-again a contradiction. Hence there are infinitely many primes.

On a personal note, my love affair with mathematics began by seeing the power and beauty of this particular proof. If mathematics could be represented by one theorem, it would be Euclid’s theorem ,which reflects the force as well as beauty of mathematics in a delicate balance.

Happy thoughts!

 

p/s: Another area of interest which deserves a blog of its own is economics. I will start an economics blog soon.

Goodchild: There must be. Your way, the way of intelligence is the way to destruction. You made man make that choice, you made him violate the natural law.
Sky: No, human life has scorned both of us. The chaos to come is of man’s own making. Neither you or I can help him now.

–From movie: Sky(1976)

Advertisements

Leave a comment

Filed under Blogroll, Uncategorized

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s